Question

Find triangle ABC in the given figure ​

Answer 1

Answer:

A = 15° ,∠B = 55° & ∠C = 110°

Step-by-step explanation:

Finding x :

∠A + ∠B = ∠D

15° + (2x + 3)° = (5x - 60)°

⇒15° + 2x + 3° = 5x - 60°

⇒18° + 2x = 5x - 60°

⇒18° + 60° = 5x - 2x

⇒78° = 3x

⇒78°/3 = x

⇒26° = x

.°. x = 26°

Finding the Angles :

• ∠A = 15°
• ∠B = (2x - 3)° → (2 × 26 + 3)° → (52 + 3)° → 55°
• ∠D = (5x - 60)° → (5 × 26 - 60°) → (130-60°) →70°

Finding ∠C

∠A + ∠B + ∠C = 180°

➣ 15° + 55° + ∠C = 180°

➣ 70° + ∠C = 180°

➣∠C = 180° - 70°

➣∠C = 110°.

Hence, ∠A = 15° ,∠B = 55° & ∠C = 110°.

Knowledge used :

• The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
• The sum of all the angles of a triangle is 180°.

Answer 2

☆Answer☆

Here,

∠BAC = 15°

∠ABC = (2x+3)°

∠BCD = (5x-60)°

Now,

∠BAC+∠ABC = ∠BCD (The exterior ∠ of a triangle is equal to the sum of the two opposite interior ∠)

15°+(2x+3)° = (5x-60)°

18+2x = 5x-60

2x-5x = -60-18

-3x = -78

x = 26°

Finding the angles:

∠BAC = 15°

∠ABC = (2×26+3) = 55°

∠BCD = (5×26-60) = 70°

Now,

∠BCD+∠BCA = 180° (Linear Pairs)

70°+∠BCA = 180°

∠BCA = 180-70

∠BCA = 110°

Hence, ∠A = 15°, ∠B = 55° and ∠C = 110°.

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